Fact-checked by Grok 2 weeks ago

Diffractometer

A diffractometer is an instrument designed to measure the angles and intensities of diffracted waves—typically X-rays, neutrons, or electrons—produced by their interaction with crystalline or polycrystalline materials, thereby enabling the determination of atomic and molecular structures through analysis of diffraction patterns.^[1] These devices operate on the principle of elastic, coherent scattering from crystal lattices, often referred to as Bragg diffraction, and can function in reflection or transmission geometries to accommodate various sample types, including powders, thin films, and single crystals.^[2]^[3] The foundational principles of diffractometry trace back to the early 20th century, beginning with Max von Laue's 1912 discovery of X-ray diffraction by crystals, which demonstrated that X-rays behave as electromagnetic waves with wavelengths comparable to atomic spacings and earned him the Nobel Prize in Physics in 1914.^[4] This breakthrough was rapidly advanced by the independent development of powder diffraction techniques: Peter Debye and Paul Scherrer introduced the method in 1916 using finely ground crystalline powders to produce characteristic ring patterns on photographic film, while Albert Hull devised a similar approach in 1917 at General Electric for analyzing metal structures.^[5]^[6] Early instruments relied on ionization chambers or film for detection, but post-World War II innovations, such as automated goniometers and scintillation counters in the 1950s, transformed diffractometers into precise, high-throughput tools for quantitative analysis.^[7] Modern diffractometers encompass a range of configurations tailored to specific applications, including laboratory-based X-ray powder diffractometers (XRD) for routine phase identification and crystallite size estimation, and synchrotron or neutron variants for enhanced resolution in complex systems.^[8] Single-crystal diffractometers, often featuring multi-circle goniometers to precisely orient samples, are crucial for solving detailed molecular structures in fields like pharmaceutical development and protein crystallography.^[9] Widely employed in materials science, chemistry, geology, and biology, these instruments provide non-destructive characterization essential for advancing technologies from semiconductors to drug discovery, with ongoing improvements in detector technology and software enabling faster and more accurate structural insights.^[10]^[11]

Fundamentals

Definition and Scope

A diffractometer is a scientific instrument designed to measure the angles and intensities of diffraction patterns generated when a beam of radiation, such as X-rays, neutrons, or electrons, interacts with a crystalline or polycrystalline sample.^[12] This measurement enables the analysis of the sample's internal structure by capturing the scattered radiation's characteristics.^[13] The term "diffractometer" originates from the combination of "diffraction," referring to the bending of waves around obstacles or through apertures, and "meter," indicating a device for measurement, thus emphasizing its role in quantifying diffracted beams.^[14] Diffractometers find primary application in crystallography, materials science, and chemistry for elucidating atomic and molecular structures, identifying phase compositions, and assessing physical properties like crystallinity and texture in various substances.^[2] These instruments operate in both conventional laboratory environments and high-flux synchrotron sources, accommodating diverse sample types from powders to single crystals.^[15] The technique underpins the diffraction phenomenon, where incident radiation interferes constructively at specific angles due to the periodic atomic lattice (detailed in Principles of Diffraction).^[16]

Principles of Diffraction

Diffraction is a fundamental wave phenomenon in which waves, such as electromagnetic radiation or matter waves, bend around obstacles or spread through apertures, resulting in interference patterns when these waves interact with periodic structures like the atomic lattices in crystals.^[17] This bending arises from the wave nature of the radiation, where each point on a wavefront acts as a secondary source of spherical wavelets, leading to constructive and destructive interference that produces observable patterns.^[18] In the context of crystallography, diffraction occurs when waves encounter the regular array of atoms in a crystal, causing the waves to scatter in specific directions determined by the lattice geometry. A key principle governing this process is Bragg's law, which describes the condition for constructive interference in the diffraction from crystal planes. Derived by considering the path length difference between waves reflected from successive atomic planes, the law states that for maximum intensity, the difference must be an integer multiple of the wavelength. Specifically, if a monochromatic wave of wavelength \lambda is incident at an angle \theta to a set of crystal planes separated by distance d, the path difference is $2d \sin \theta, leading to the equation n\lambda = 2d \sin \theta, where n is a positive integer representing the order of diffraction.^[19] This relation arises because waves scattered from deeper planes travel an extra distance compared to those from the surface plane, and constructive interference occurs only when this extra path aligns in phase with the incident wave.^[20] The effectiveness of diffraction in probing crystal structures relies on using radiation whose wavelength matches the atomic scale, typically around 0.1 nm (1 Å), comparable to interatomic distances in solids. Monochromatic X-ray beams, for example, with wavelengths in this range, interact with the electron clouds around atoms to produce sharp diffraction spots or rings, revealing the periodic arrangement of the lattice.^[21] This scale ensures that the interference effects are pronounced, as the wavelength is neither much larger (which would cause diffuse scattering) nor much smaller (which would limit observable orders) than the structural features.^[3] Diffraction must be distinguished from general scattering: while scattering refers to the redirection of waves by individual atoms or particles, often resulting in diffuse patterns due to incoherent or random interactions, diffraction specifically involves elastic scattering from an ordered array of scatterers, such as a crystal lattice, producing discrete, interference-based patterns.^[22] In crystals, this ordered scattering amplifies constructive interference at specific angles dictated by Bragg's law, enabling the resolution of structural details, whereas disordered materials yield only broad scattering halos.^[23]

History

Early Discoveries

The discovery of X-rays in 1895 by Wilhelm Conrad Röntgen marked the foundational breakthrough that enabled subsequent diffraction studies. While experimenting with cathode rays in a low-pressure gas tube at the University of Würzburg, Röntgen observed an unexpected fluorescence on a nearby screen, leading him to identify a new form of penetrating radiation on November 8, 1895.^[24] This radiation, which he termed "X-rays" due to its unknown nature, demonstrated variable transparency through materials and was the first to produce shadow images of internal structures, such as bones.^[24] The first deliberate X-ray diffraction experiment occurred in 1912, conducted by Max von Laue, Walter Friedrich, and Paul Knipping at the University of Munich. Motivated by the wave properties of X-rays and the periodic structure of crystals, they directed a beam of X-rays through a single crystal of zinc blende (sphalerite, ZnS) and recorded the resulting pattern on a photographic plate, revealing a symmetrical array of spots that confirmed both the wave nature of X-rays and the atomic lattice arrangement in crystals.^[25] This Laue experiment provided empirical proof of crystal periodicity and opened the path for using diffraction as a structural probe.^[26] Building on Laue's findings, William Henry Bragg and his son William Lawrence Bragg advanced the field through their work on X-ray reflection from crystal planes between 1912 and 1913. The younger Bragg developed a reflection-based interpretation of diffraction patterns, proposing that X-rays reflect specularly from atomic planes at specific angles, which allowed for the indexing and analysis of patterns to deduce crystal structures.^[27] The elder Bragg constructed an early X-ray spectrometer to measure these reflections quantitatively, enabling studies of simple salts and molecules.^[27] Their collaborative efforts, which included the formulation now known as Bragg's law relating wavelength, plane spacing, and reflection angle, earned them the 1915 Nobel Prize in Physics for services in crystal structure analysis.^[27] Initial experiments with polycrystalline materials emerged in 1916 with the Debye-Scherrer method, developed by Peter Debye and Paul Scherrer at the University of Göttingen. To extend diffraction to powders lacking single-crystal orientation, they irradiated fine polycrystalline samples, such as lithium fluoride, with X-rays from a copper anticathode tube and captured the resulting conical diffraction beams on a cylindrical photographic film wrapped around the sample, producing characteristic rings that could be analyzed for lattice parameters. This technique democratized structural studies by accommodating readily available powder forms of materials.

Instrument Development

The development of powder diffraction instruments began with early prototypes designed to measure X-ray diffraction patterns more systematically than previous photographic methods. In 1919, Albert W. Hull at General Electric Laboratories introduced a powder camera that utilized photographic film to record the diffraction rings, marking a significant advancement in capturing diffraction data from polycrystalline samples for chemical analysis.^[6] This innovation built on Hull's earlier work in 1917, where he independently demonstrated the powder method for determining crystal structures, such as that of iron, enabling broader application to materials without single crystals.^[28] Concurrently, Peter Debye and Paul Scherrer contributed foundational techniques in 1916 by developing the Debye-Scherrer powder method, which used cylindrical cameras to record diffraction rings from finely ground samples.^[5] A pivotal advancement came in 1926 when Wheeler P. Davey constructed the first X-ray powder diffractometer at Penn State University, incorporating a goniometer for angular scanning and an ionization chamber for intensity measurement.^[29] By the mid-20th century, instrumental refinements addressed limitations in detection and precision. In the 1930s, Geiger-Müller counters began replacing photographic film and ionization chambers, offering real-time intensity measurements and improved sensitivity for weak diffraction signals, as demonstrated in early applications for measuring X-ray diffraction patterns of materials like sodium chloride.^[30] The 1940s saw advancements in goniometer designs, with engineers like Lindemann and Trost developing mechanisms for automated angular control, allowing precise scanning of diffraction angles and reducing manual errors in single-crystal studies.^[31] These goniometers, often integrated with Geiger counters, facilitated more reliable data collection during World War II-related materials research. Post-World War II, the focus shifted to commercialization and expansion to other radiation types, transforming diffractometers into accessible laboratory standards. In the 1950s, Philips (under its Norelco brand) introduced commercial X-ray diffractometers, such as the 1954 model with enhanced resolution and wider angular range, making the technology routine for industrial and academic use in phase identification.^[32] For neutron diffraction, Ernest O. Wollan and Clifford G. Shull pioneered the first such instrument in 1946 at Oak Ridge National Laboratory's X-10 graphite reactor, adapting double-axis spectrometers for powder studies and revealing magnetic structures inaccessible to X-rays.^[33] By the 1960s, automation accelerated with computer integration; systems like the computer-controlled X-ray diffractometer used IBM 1620 processors for real-time data acquisition and analysis, enabling stepwise scanning and pattern indexing without manual intervention.^[34] These milestones, driven by figures like Debye, Scherrer, Hull, and Davey, established diffractometers as essential tools for structural elucidation.

Types

X-ray Diffractometers

X-ray diffractometers are the most prevalent instruments in diffraction analysis, utilizing X-rays to probe the atomic structure of materials through interactions governed by principles of diffraction.^[35] They are categorized into primary subtypes based on sample form: powder diffractometers for polycrystalline materials and single-crystal diffractometers for well-ordered crystals. Powder diffractometers employ geometries such as Debye-Scherrer or Bragg-Brentano to capture diffraction patterns from randomly oriented crystallites.^[35] In Bragg-Brentano geometry, the reflection mode positions the sample in the plane of the goniometer circle, with the X-ray source and detector moving in a theta-2theta scan to maintain the Bragg condition.^[35] This contrasts with transmission modes like Debye-Scherrer, where the beam passes through a capillary-held sample, allowing for cylindrical symmetry in the diffraction rings.^[35] Radiation sources in X-ray diffractometers typically feature copper anodes emitting Cu K\alpha radiation with a wavelength of \lambda = 1.54 Å, selected for its balance of penetration and resolution in routine laboratory settings.^[35] For enhanced intensity and tunable wavelengths, synchrotron sources provide orders-of-magnitude higher brilliance, enabling studies of weakly scattering samples.^[35] Sample preparation for powder diffractometry involves grinding the material to fine particles, often using a mortar and pestle to achieve random orientation and minimize preferred alignment effects.^[36] Single-crystal diffractometers, designed for precise lattice orientation, utilize four-circle or kappa goniometer geometries to adjust the sample across multiple axes.^[9]^[37] The four-circle setup defines positions via angles 2\theta, \chi, \phi, and \Omega, while kappa geometry incorporates a tilting axis for improved accessibility to reciprocal space.^[9]^[37] Data collection often employs omega scans, rotating the crystal around the omega axis in small increments to map diffraction intensities.^[9] Crystals are mounted on thin glass fibers or nylon loops affixed to goniometer pins, ensuring minimal absorption and precise centering, with typical sizes ranging from 50 to 500 \mum.^[9]

Neutron and Electron Diffractometers

Neutron diffractometers utilize thermal neutrons generated from nuclear reactors or spallation sources to probe atomic and magnetic structures in materials.^[38] Reactors, such as the 58 MW high-flux reactor at the Institut Laue-Langevin (ILL) in Grenoble, France, produce continuous neutron beams with fluxes up to 10^15 neutrons per second per cm², enabling high-resolution diffraction experiments on bulk samples.^[39] Spallation sources, like the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory, generate pulsed neutron beams through proton bombardment of heavy metal targets, offering time-of-flight diffraction for broader energy ranges.^[38] These instruments excel in locating light elements like hydrogen and lithium due to neutrons' sensitivity to nuclear scattering lengths, which contrast sharply between isotopes (e.g., hydrogen: -3.74 fm, deuterium: +6.67 fm), allowing isotopic substitution studies without altering electron density.^[40] Additionally, neutrons interact with magnetic moments, making them ideal for determining magnetic structures, such as spin densities in coordination compounds like iron clusters.^[41] A prominent example is the triple-axis spectrometer, which employs three single-crystal monochromators to select incident and scattered neutron wavelengths, enabling precise measurements of phonon dispersions or magnetic excitations in reciprocal space.^[38] Facilities like the NIST Center for Neutron Research feature multiple triple-axis spectrometers alongside single-crystal and powder diffractometers, supporting studies on materials from the Cold Neutron Research Facility's 20 MW reactor.^[42] Neutron diffraction thus provides complementary data to other techniques by penetrating deeply into samples (centimeters for many materials) and revealing bulk properties insensitive to surface effects.^[41] Electron diffractometers, often integrated into transmission electron microscopes (TEM), employ accelerated electrons with de Broglie wavelengths around 0.0025 nm at 200 keV for atomic-scale structural analysis.^[43] Selected area electron diffraction (SAED) selects specific regions of thin samples (typically 10-100 nm thick) to generate diffraction patterns, achieving resolutions down to 0.7 Å for nanocrystals as small as tens of nanometers.^[43] This setup offers high spatial resolution for nanoscale imaging but is limited by electrons' strong interactions with matter, restricting penetration to micrometer depths in low-Z materials and requiring electron-transparent foils prepared via ultramicrotomy or ion milling.^[44] Lab-based TEM systems, such as those equipped with aberration-corrected lenses, enable routine 3D electron diffraction tomography for reconstructing structures of beam-sensitive organics or inorganics.^[43] Recent advances have introduced standalone electron diffractometers, such as the XtaLAB Synergy-ED developed by Rigaku and JEOL (launched in 2023), which provide dedicated platforms for 3D electron diffraction on submicron-sized crystals without the need for full TEM integration. These instruments feature automated workflows from data collection to structure solution, enhancing accessibility for routine analysis of nanocrystals in fields like pharmaceuticals and materials science.^[45] In contrast to neutron methods, electron diffraction prioritizes high-resolution patterns from localized volumes in thin specimens, ideal for heterogeneous nanomaterials, while neutrons favor bulk isotopic and magnetic contrast in larger samples.^[41]^[44] These complementary approaches enhance overall structural elucidation, with neutron facilities like ILL serving international users for large-scale experiments and electron systems enabling accessible, in-house nanoscale investigations.^[39]

Instrumentation

Key Components

A diffractometer's core functionality relies on several essential hardware elements: the radiation source, which generates the incident beam; the sample stage, which precisely positions the specimen; the detectors, which capture diffracted radiation; and the optics, which condition the beam for optimal interaction and resolution. These components are interconnected to enable accurate measurement of diffraction patterns, primarily using X-ray, neutron, or electron radiation, though configurations vary by type.^[16] The radiation source is typically an X-ray tube consisting of a heated filament cathode that emits electrons, accelerated toward a metal anode target such as copper (Cu), iron (Fe), or molybdenum (Mo) to produce characteristic X-rays via bremsstrahlung and characteristic emission.^[16] Sealed tubes operate at currents of 10–100 mA for standard laboratory use, while rotating anode tubes provide higher flux by spinning the anode to dissipate heat, enabling brighter beams for demanding applications. To achieve monochromatic radiation, such as Cu Kα at 1.5406 Å, β-filters like nickel (Ni) foil absorb unwanted Kβ wavelengths, and monochromators—either single crystals (e.g., graphite) for Bragg reflection or multilayer optics—further purify the beam by selecting specific wavelengths.^[16] The sample stage centers on a goniometer, a motorized mechanical assembly that enables precise angular positioning of the specimen to satisfy diffraction conditions.^[46] In advanced setups, an Eulerian cradle provides multi-axis control (typically four or six circles, including χ, φ, ω, and 2θ rotations) for orienting single crystals or complex samples in three dimensions.^[47] Sample holders are tailored to the material form: flat plates or cavities for powders to ensure random orientation, capillary tubes for minimal preferred orientation, or specialized mounts for thin films and single crystals to maintain alignment without deformation.^[16] Detectors convert incoming X-ray photons into measurable electrical signals, quantifying intensity and spatial distribution to reconstruct diffraction patterns.^[48] Scintillation counters, using materials like NaI(Tl) coupled to photomultiplier tubes, provide point detection with high efficiency for scalar intensity measurements but require scanning.^[48] Position-sensitive detectors (PSD), often gas-filled proportional counters with delay-line anodes, capture linear (1D) profiles over a wide angular range (up to 120°) simultaneously, improving data acquisition speed and signal-to-noise ratio.^[49] Area detectors, such as charge-coupled devices (CCD) with phosphor screens or image plates (e.g., storage phosphor technology), enable 2D imaging of Debye cones or full reciprocal space mapping, essential for rapid collection from polycrystalline or single-crystal samples.^[48] Optics components shape and collimate the beam to minimize divergence, aberrations, and background noise while maximizing flux on the sample. Incident and receiving slits, adjustable in width (e.g., 0.1–1 mm), control beam divergence and resolution in Bragg-Brentano geometry, defining the illuminated sample area.^[50] Soller collimators, arrays of closely spaced parallel plates, limit axial divergence to ~0.5°–1°, preventing off-axis scattering from entering the detector.^[50] Göbel mirrors, parabolic multilayer optics (e.g., W/Si with graded d-spacings of ~2–10 nm), focus divergent tube emission into a parallel or slightly convergent beam while monochromatizing, reducing geometric errors in thin-film or powder analysis.

Operational Principles

The operation of a diffractometer involves a structured experimental workflow starting with sample mounting. For powder diffraction experiments, the sample is typically prepared as a fine crystalline powder and pressed into a holder, such as a zero-background plate or cavity, to create a smooth, flat surface flush with the holder to minimize preferred orientation effects, ensuring the surface is parallel to the goniometer plane. Solid or thin-film samples may be mounted using adhesives like carbon tape on a substrate, ensuring the surface is parallel to the incident beam plane. Once mounted, the sample holder is inserted into the goniometer stage, and the instrument doors are securely closed to engage safety interlocks.^[51]^[52] Alignment follows mounting and includes zero-point calibration to correct for any offsets in the angular scales of the goniometer and detector. This is achieved by scanning a reference peak or direct beam and adjusting the sample height (z-axis) and tilt (ω) until maximum intensity is obtained, often targeting half the peak maximum for optimal positioning. Beam optimization then adjusts collimators, slits, and monochromators to balance intensity and resolution, preventing divergence errors while maximizing flux on the sample. Key components such as the X-ray tube, goniometer, and detector are configured during this phase to ensure precise θ-2θ coupled motion.^[52]^[16] Data acquisition proceeds in selected scanning modes: step-scan, where the goniometer pauses at each angular position for a fixed exposure time, or continuous scan, where it moves at a constant rate (e.g., 1°/min) while the detector integrates signal over the motion. Typical parameters include an angular range of 5° to 150° 2θ to cover common Bragg reflections, step sizes of 0.01° to 0.1° 2θ for resolution balancing speed and detail, and exposure times of 1 to 10 seconds per step to achieve sufficient count statistics without excessive noise. Background subtraction is performed during or post-collection by measuring a blank scan or fitting a polynomial model to the baseline, removing contributions from air scatter, sample fluorescence, or instrument noise.^[53]^[54]^[55] Safety protocols are integral to operation, given the ionizing radiation from the X-ray source. Instruments feature lead-lined enclosures and interlocked shielding to contain the primary beam, with operators required to verify warning lights, radiation monitors, and door seals before energizing the system; surveys for leakage are conducted after any modifications. High-voltage precautions for the X-ray tube include gradual ramping of voltage (e.g., in 5-10 kV increments with pauses) and current to 40 kV and 40 mA, respectively, to prevent arcing or electrical hazards, and all personnel must wear dosimeters while adhering to ALARA principles of time, distance, and shielding minimization.^[56]^[51] Common error sources in diffractometer operation include peak broadening from finite crystallite size in the sample or instrumental factors like beam divergence and detector resolution, which can distort line profiles and shift positions. These are addressed through regular calibration using standards such as NIST SRM 660c, a lanthanum hexaboride powder certified for line position and shape accuracy, enabling corrections for systematic offsets and broadening contributions.^[57]^[58]

Applications

Structural Analysis

Diffractometers play a central role in structural analysis by enabling the determination of atomic arrangements in crystalline materials through the interpretation of diffraction patterns. In single-crystal analysis, the process begins with indexing the reflections from collected diffraction data to identify the unit cell dimensions and orientation, followed by space group determination using systematic absences or statistical tests on intensity distributions.^[59] Once the space group is established, structure solution proceeds via Patterson methods, which utilize the Fourier transform of squared structure factors to locate heavy atoms by interpreting interatomic vectors, or direct methods, which probabilistically estimate phases based on atomicity constraints to generate electron density maps.^[60] Refinement of the resulting model against observed intensities is typically performed using least-squares minimization, often with software such as SHELXL, which incorporates full-matrix refinement on F² to optimize atomic positions, thermal parameters, and occupancy factors.^[61] For powder diffraction data, where overlapping reflections complicate analysis, structure solution relies on Rietveld refinement for known phases, involving profile fitting of the entire diffraction pattern to quantify phase abundances and lattice parameters by minimizing differences between observed and calculated intensities.^[62] Ab initio methods for unknown structures employ direct-space approaches, such as Monte Carlo simulations or genetic algorithms, to search for trial models that match the powder pattern, followed by Rietveld refinement to achieve convergence.^[63] These techniques are particularly valuable for polycrystalline samples where single crystals are unavailable, allowing extraction of structural details like bond lengths and angles with precision comparable to single-crystal methods when data quality is high. In protein crystallography, diffractometers facilitate the elucidation of biomolecular structures, as seen in entries from the Protein Data Bank (PDB), such as the insulin-zinc complex (PDB ID: 1FU2), the first protein structure solved from high-resolution X-ray powder diffraction data, revealing detailed folding and ligand interactions.^[64] Similarly, small-molecule structures, like organic compounds or organometallics, benefit from routine single-crystal analysis to confirm stereochemistry and conformational preferences, contributing to thousands of annually deposited structures in crystallographic databases.^[65] The quality of structural models is assessed using R-factors, where R1 measures the agreement between observed and calculated structure factor amplitudes (typically below 5% for well-refined small-molecule structures), and wR2 provides a weighted version incorporating all data for a more robust goodness-of-fit evaluation, often around 10-15%.^[66] Resolution limits for X-ray diffraction generally reach ~0.5 Å for high-quality small-molecule crystals, enabling visualization of individual atoms and hydrogen positions, though protein structures often resolve to 1-2 Å due to disorder.^[67]

Materials Characterization

Diffractometers play a crucial role in materials characterization by enabling the identification and quantification of phases in polycrystalline materials such as alloys and ceramics. Phase identification involves comparing measured X-ray diffraction (XRD) patterns to reference databases like the International Centre for Diffraction Data (ICDD) Powder Diffraction File (PDF), which contains over 1 million entries for known crystalline phases. This qualitative analysis matches peak positions and intensities to determine the presence of specific phases, while quantitative methods, such as the Rietveld refinement, estimate phase abundances by fitting the entire diffraction pattern. In alloys, this technique distinguishes between matrix and precipitate phases, aiding in quality control for manufacturing processes.^[68]^[50] Texture analysis using diffractometers assesses preferred crystallographic orientations in materials, often visualized through pole figures that map the distribution of lattice planes relative to the sample surface. These figures are constructed by measuring diffraction intensities at varying sample rotations and tilts, revealing anisotropies that influence mechanical properties like strength and ductility in rolled metals or extruded polymers. For residual stress evaluation, the sin²ψ method exploits the tilt-dependent shift in diffraction peaks to quantify lattice strains. Under plane stress conditions and assuming isotropic elasticity, the interplanar spacing d_{\psi} varies linearly with \sin^2\psi according to Hooke's law, where the strain \epsilon_{\psi} = (d_{\psi} - d_0)/d_0 relates to the applied stress \sigma as \epsilon_{\psi} = \frac{1+\nu}{E} \sigma \sin^2\psi - \frac{\nu}{E} (\sigma_1 + \sigma_2), with E as Young's modulus, \nu as Poisson's ratio, and d_0 as the stress-free spacing. The stress is then derived from the slope m of the d_{\psi} versus \sin^2\psi plot: \sigma = \frac{E}{1+\nu} m, where m \approx \Delta d / d for the strain range. This approach is widely applied in engineering to detect stresses in welds or machined components.^[69]^[70]^[71]^[72] For thin films and surface characterization, grazing-incidence XRD (GIXRD) enhances sensitivity by directing the X-ray beam at a shallow angle (typically 0.5–1°) just above the critical angle for total external reflection, limiting penetration to 1–100 nm and suppressing substrate signals. This configuration allows measurement of in-plane lattice parameters, enabling determination of layer thickness through angle-dependent intensity oscillations and assessment of epitaxial quality by detecting azimuthal alignments between film and substrate. GIXRD is particularly valuable for multilayer coatings in electronics, where it reveals strain gradients and interfacial epitaxy without destructive sectioning.^[73]^[74] In pharmaceutical applications, diffractometers facilitate polymorph screening by distinguishing crystalline forms of active ingredients, which can differ in solubility and bioavailability; for instance, XRD patterns uniquely fingerprint forms like anhydrous versus hydrated variants of carbamazepine. Similarly, in forensics, XRD matches diffraction signatures of unknown materials—such as pigments in paints or minerals in soils—to reference libraries, supporting evidence linkage in criminal investigations, as seen in geological sample analysis for soil provenancing. Data collection in these contexts relies on standard θ-2θ scans to generate reliable patterns for database comparison.^[75]^[76]^[77]^[78]

Advances and Limitations

Modern Developments

Since the 2000s, the integration of synchrotron radiation and X-ray free-electron lasers (XFELs) has revolutionized diffractometry by enabling time-resolved studies of dynamic processes in materials and biomolecules. Facilities such as the European Synchrotron Radiation Facility (ESRF) and the Linac Coherent Light Source (LCLS) provide ultrabright, ultrafast X-ray pulses that capture structural changes on femtosecond to picosecond timescales, minimizing radiation damage through "diffraction before destruction" techniques.^[79] For instance, these sources have facilitated investigations into protein folding and conformational dynamics, where serial snapshots reveal transient intermediates previously inaccessible with conventional lab-based diffractometers.^[80] This advancement has expanded diffractometry's scope to real-time monitoring of photochemical reactions and phase transitions in functional materials.^[81] Automation and advanced software have significantly enhanced the efficiency and throughput of diffractometers, particularly in high-volume structural analyses. Robotic sample changers, integrated into systems like those at synchrotron beamlines, allow for unattended handling of hundreds of samples, reducing setup times from hours to minutes and enabling 24/7 operation.^[82] Complementing this hardware, artificial intelligence (AI) and machine learning algorithms have been developed for automated phase identification and pattern refinement, achieving over 95% accuracy in matching diffraction data to known crystal structures without manual intervention.^[83] These tools, such as ML-driven workflows in powder X-ray diffraction (XRD), streamline data processing by predicting phase compositions in complex mixtures, thereby accelerating materials discovery in fields like pharmaceuticals and energy storage.^[84] Hybrid diffractometer systems have emerged to address limitations in analyzing disordered materials, combining traditional XRD with pair distribution function (PDF) analysis for comprehensive structural insights. PDF methods, which utilize total scattering data to probe atomic pair correlations, excel in characterizing amorphous and nanocrystalline phases where Bragg peaks are absent, revealing local order in glasses and polymers.^[85] Portable and handheld XRD units, weighing under 5 kg and powered by batteries, extend these capabilities to field applications, such as on-site mineral identification in mining or cultural heritage analysis, with detection limits comparable to lab instruments.^[86] Key milestones include the 2010s surge in serial crystallography, pioneered at XFELs, which democratized microcrystal studies by indexing thousands of patterns per experiment.^[87] In the 2020s, pixel array detectors like advanced hybrid photon counting systems have enabled sub-angstrom resolutions in optimized setups and readout speeds exceeding 1000 frames per second, supporting higher flux handling and reduced noise in dynamic experiments.^[88]

Challenges and Future Directions

One major limitation of X-ray diffractometers is radiation damage to samples, particularly organic and biological materials, where high-intensity X-rays can cause structural degradation, decarboxylation, or breakage of disulfide bonds, reducing diffraction quality and limiting data collection time.^[89] This issue is exacerbated in macromolecular crystallography, where even brief exposures can lead to specific damage sites that compromise resolution.^[90] Additionally, diffractometry requires high-quality, well-ordered crystals, which can be difficult to obtain for flexible or heterogeneous biomolecules, often necessitating extensive optimization efforts.^[91] Advanced sources like synchrotrons, while providing intense beams for better signal-to-noise, incur high operational costs due to their energy demands and infrastructure needs, restricting access for many researchers.^[92] For disordered systems, such as amorphous materials or imperfect crystals, resolution is inherently limited by weak and diffuse scattering patterns, making atomic-level structure determination challenging without complementary high-energy techniques.^[93] High-throughput diffractometry experiments generate vast datasets, leading to data overload that strains computational resources and slows analysis, especially when integrating multi-modal inputs from automated screening.^[94] Interpreting diffraction patterns from complex multiphase mixtures poses further challenges, as overlapping peaks from preferred orientations, microabsorption, and broad reflections complicate phase identification and quantitative analysis.^[95] Future directions include integrating diffractometry with cryo-electron microscopy (cryo-EM) and nuclear magnetic resonance (NMR) for hybrid structure determination, where low-resolution cryo-EM maps guide X-ray phasing or NMR provides dynamic constraints to resolve ambiguities in crystal structures.^[96] Developments in tabletop neutron sources, driven by compact laser-plasma accelerators, aim to enable accessible neutron diffraction for hydrogenous materials without relying on large facilities.^[97] Artificial intelligence, particularly convolutional neural networks, is advancing real-time analysis by automating phase identification and pattern interpretation from diffraction data, potentially reducing processing times from hours to seconds; recent advances include neural networks solving the phase problem directly from diffraction patterns at resolutions as low as 2 Å.^[98]^[99] Efforts to address the environmental impact of synchrotron operations, which consume significant electricity, include sustainable designs such as energy-efficient upgrades, renewable energy integration, and waste heat recovery systems to reduce carbon footprints while maintaining high-flux capabilities.^[100]

References

[1]
Section 2.1.2. Scope and terminology
An X-ray (powder) diffractometer is by definition an instrument for measuring X-ray diffraction phenomena (from powders), where `diffraction' is defined as ...
[2]
Diffractometers - an overview | ScienceDirect Topics
Diffractometers are used in X-ray diffraction to characterize crystalline samples, and can operate in reflection or transmission modes.
[3]
XRD Basics - UPenn Physics
Jul 16, 2025 · X-ray diffraction (XRD) is a non-destructive technique for analyzing the structure of materials, primarily at the atomic or molecular level.What is x-ray diffraction? · What are the components of...
[4]
Max von Laue – Facts - NobelPrize.org
Experiments confirmed von Laue's idea. This demonstrated that X-rays could be described as waves. The method also made it possible to use diffraction patterns ...
[5]
A Century of Powder Diffraction: a Brief History - Etter - 2014
Dec 3, 2014 · Almost a century has passed since the pioneering work of Debye, Scherrer, and Hull and their first powder X-ray diffraction experiments in ...
[6]
100 years of the X-ray powder diffraction method | OUPblog
Sep 20, 2016 · It was introduced as early as 1919 by Hull as a new method of “X-ray chemical analysis”. The powder diagram of a given substance is indeed ...
[7]
(IUCr) The Development of X-ray Diffraction in USA
Langdon, Frazer and Pepinsky described the design of a new type of neutron diffractometer in 1956, and in 1959 Langdon and Frazer published design details of an ...<|control11|><|separator|>
[8]
X-Ray Diffractometer (XRD) - The University of Akron
X-ray diffraction (XRD) is a nondestructive technique for characterizing crystalline materials or materials with some crystalline domains in them.
[9]
Single-crystal X-ray Diffraction - SERC (Carleton)
May 17, 2007 · Single-crystal diffractometers use either 3- or 4-circle goniometers. These circles refer to the four angles (2θ, χ, φ, and Ω) that define the ...
[10]
How do X-ray diffractometers work? - Stresstech
An X-ray diffractometer, or XRD machine, is a device for analyzing and measuring the structure of materials.
[11]
X-Ray Diffractometer (XRD)
An X-Ray Diffractometer (XRD) characterizes materials using X-Ray diffraction, typically powders and thin films, to measure internal dimensions. It is not for ...Missing: definition | Show results with:definition
[12]
DIFFRACTOMETER Definition & Meaning - Merriam-Webster
an instrument for analyzing the structure of a usually crystalline substance from the scattering pattern produced when a beam of radiation or particles
[13]
Diffractometers - an overview | ScienceDirect Topics
A diffractometer is an instrument used in this process, capable of analyzing small samples, often in a destructive manner. AI generated definition based on: ...
[14]
DIFFRACTOMETER Definition & Meaning - Dictionary.com
an instrument that is used to study atomic crystal structure by measuring the angles at which x-rays, neutrons, or electrons are diffracted by matter.
[15]
X-Ray Diffractometer | NIST
The Bruker D8 defractometer is a general purpose X-ray diffraction system. The instrument features easy reconfiguration of the X-ray optics for a variety of ...Missing: definition | Show results with:definition
[16]
X-ray Powder Diffraction (XRD) - SERC (Carleton)
Jun 15, 2018 · X-ray powder diffraction (XRD) is a rapid analytical technique primarily used for phase identification of a crystalline material and can provide information on ...
[17]
Light and Color - Diffraction of Light - Molecular Expressions
Nov 13, 2015 · Diffraction is often explained in terms of the Huygens principle, which states that each point on a wavefront can be considered as a source ...
[18]
[PDF] WILLIAM LAWRENCE BRAGG The Dawn of X-ray Crystallography
WLB's paper subsequently appeared in print in February 1913**. The importance of this work cannot be overstated, for it heralded a revolution in the scientific ...
[19]
X-ray Basics | Material Research Laboratory - UCSB MRL
Because the wavelength of x-rays is comparable to the size of atoms, they are ideally suited for probing the structural arrangement of atoms and molecules ...X-Ray Basics · Powder Diffraction · Thin Film Diffraction<|control11|><|separator|>
[20]
Crystallography. Scattering and diffraction
In the crystal case the scattering effect is known as diffraction. Note how the scattering phenomenon reflects the internal order of the sample -- the ...
[21]
Wilhelm Conrad Röntgen – Biographical - NobelPrize.org
Wilhelm Conrad Röntgen was born on March 27, 1845, at Lennep in the Lower Rhine Province of Germany, as the only child of a merchant in, and manufacturer of, ...
[22]
Disputed discovery: the beginnings of X-ray diffraction in crystals in ...
Apr 20, 2012 · Max von Laue (1879–1960) with diffraction patterns obtained from crystals of copper sulfate (top left) and zinc blende (bottom right), and the ...
[23]
Perspectives: X-ray's identity becomes crystal clear - NobelPrize.org
An unusual and unorthodox series of scientific discussions in a café led to Max von Laue's ingenious experiment that unmasked the true identity of X-rays.
[24]
Speed read: Crystal patterns made plane and simple - NobelPrize.org
When Max von Laue showed that X-rays are diffracted in crystals and form characteristic patterns on photographic film, he proved in a single experiment that X ...
[25]
The contributions of Albert W. Hull to X-ray powder diffraction at one ...
Jan 18, 2017 · For the first example, Hull recorded the powder diffraction pattern “.. of a sample of sodium fluoride, taken from the stock, labelled 'C.P.'”.
[26]
A Type of Geiger‐Müller Counter Suitable for the Measurement of ...
These graphs duplicate the well‐known diffraction patterns of these materials, thus giving additional evidence of the reliability of the counters. Topics.
[27]
https://www.nobelprize.org/prizes/physics/1915/speedread/
[28]
1954 - The Norelco X-Ray Diffractometer | PDF - Scribd
1) The document describes a redesigned X-ray diffractometer that provides higher resolution, better measurement accuracy, and a wider diffraction angle ...<|control11|><|separator|>
[29]
A History of Neutron Scattering at ORNL
Jun 13, 2018 · Neutron scattering grew from the nuclear science of the Manhattan Project during the 1940s at what is now Oak Ridge National Laboratory (ORNL).
[30]
Computer‐Controlled Diffractometer - AIP Publishing
A standard four‐axis Geiger counter single‐crystal diffraction configuration is made automatic by attaching encoders to all shafts with provision made for ...Missing: automated | Show results with:automated<|control11|><|separator|>
[31]
[PDF] Fundamentals and applications of X-ray diffraction. Applications in ...
electrons at relativistic velocities in circular trajectories. • Bragg Brentano and Debye Scherrer are the two possible configurations of powder diffractometers.Missing: kappa Kα preparation
[32]
Sample Preparation – EAS X-Ray Diffraction ... - University of Alberta
Usually powdered XRD samples are prepared by hand grinding using a mortar and pestle. The mortar and pestle can be made out of a variety of materials such as ...
[33]
None
### Summary of Kappa Geometry, Omega Scans, and Radiation Sources in XtaLAB Synergy Diffractometers
[34]
[PDF] An Introduction to Neutron Scattering
Neutron advantages: – Wavelength comparable with interatomic spacings. – Kinetic energy comparable with that of atoms in a solid.
[35]
ILL Neutrons for Society
High-quality neutron and X-ray data acquired using red blood cells allowed researchers to establish a universal theoretical description of cell membranes.ILL at a glance · ILL science groups · Job Vacancies · The ILL high-flux reactor
[36]
[PDF] Thomas F. Koetzle Chemistry Department, Brookhaven National ...
Neutron diffraction therefore has important advantages in studies where hydrogen or other light atoms must be located, or where isotopic substitutions may be of ...
[37]
Neutron Instruments for Research in Coordination Chemistry - PMC
Neutron diffraction is the principle tool for determining magnetic structures since it gives access to the direction and size of magnetic moments and their ...
[38]
[PDF] The NIST Cold Neutron Research Facility
A diagram of the current layout of facilities around the reactor is shown in Fig. 1. Single Crystal. Dlffractometer. Polarized Beam. Dlffractometer^. Triple- ...
[39]
3D Electron Diffraction for Chemical Analysis: Instrumentation ...
Note that the 2θ ranges for a typical data set with a resolution range between 0.8 and 25 Å for these three wavelengths are 2.4°–0.08°, 1.8°–0.06°, and 1.4°– ...
[40]
The Role of Transmission Electron Microscopy in the Early ... - NIH
Dec 20, 2021 · Transmission electron microscopy images, selected area electron diffraction (SAED) and medium resolution scanning transmission electron ...
[41]
Anatomy of an X-ray diffractometer - Intro - XRD - MyScope
Most diffractometers in materials science are based on the reflection geometry where the X-ray source and detector are on the same side of the sample.<|separator|>
[42]
[PDF] Lesson 15 - CCDC
Lesson 15 covers data collection methods, including film, serial diffractometers, and area detectors, and how to submit crystals.
[43]
X-ray detection - DoITPoMS
A single point (0D), line (1D) or area (2D) detector may be used. All detectors rely on the ability of X-rays to ionise atoms, whether those are gas atoms ( ...
[44]
XRD Detectors - Malvern Panalytical
Effectively the detector becomes a cylindrical position-sensitive detector (PSD) with the versatility to accommodate different goniometer radii.
[45]
[PDF] X-RAY POWDER DIFFRACTION - XRD for the analyst
In single crystal diffraction it is defined as the lowest possible d-value, which can be measured with an instrument. In small-angle X-ray scattering it is the ...
[46]
[PDF] Operating Procedure for X-Ray Diffraction Purpose and Scope
The ideal sample will be a crystalline powder that has been pressed into the sample holder, have a smooth surface, and hold in the sample at an angle of 45 ...
[47]
https://www.ccdc.cam.ac.uk/media/resources/fanwick-selecting-crystals-goniometers-detectors.pdf
[48]
[PDF] Standard Operation Procedure (SOP) X-Ray Diffractometer ...
Choose Step or Continuous scan method. For Step you must specify a. “Preset” time. For Continuous, choose a Scan Rate using the slide bar under “Rate (deg ...
[49]
Principles and Techniques of X-Ray Diffraction (XRD) - Universallab
Esfand 18, 1403 AP · Careful mounting: Use nylon loops or glass fibers to mount crystals without damaging them. Optimization of XRD Test Parameters. Setting ...
[50]
Bruker d8 XRD Procedures
Bruker Diffrac. Eva. This program is used for processing of XRD scans, including background removal, peakfinding, and search-match procedures. Topas.
[51]
[PDF] Radiation Safety Training for X-ray Diffraction and Fluorescence ...
What is the safest precaution to take before attempting to remedy a malfunction in any component on the high voltage side (x-ray tube, high voltage cable, etc.)? ...Missing: diffractometer protocols
[52]
[PDF] 660c | Certificate - National Institute of Standards and Technology
This Standard Reference Material (SRM) is intended for use in calibration of diffraction line positions and line shapes determined through powder diffractometry ...
[53]
(PDF) Error Corrections For X-RAY Powder Diffractometry
Aug 9, 2025 · The errors involved in precision lattice parameter determination fall into three broad groups: errors that can be corrected by applying a multiplication factor ...
[54]
Single‐Crystal X‐Ray Structure Determination - Wiley Online Library
Oct 15, 2002 · This article concentrate on the use of X-ray diffraction techniques as would be necessary for the normal crystal structure investigation. A ...
[55]
[PDF] The SHELX-97 Manual
SHELX-97 contains the following six executable programs: SHELXS - Structure solution by Patterson and direct methods. SHELXL - Structure refinement (SHELXH for ...
[56]
SHELXT – Integrated space-group and crystal-structure determination
SHELXT automates routine small-molecule structure determination starting from single-crystal reflection data, the Laue group and a reasonable guess as to which ...
[57]
[PDF] Ab initio structure determination via powder X-ray diffraction
When once a meaningful model emerges, application of the Rietveld refinement procedure completes the structure determination and refinement. Recent reviews3–6 ...
[58]
Direct Methods Optimised for Solving Crystal Structure by Powder ...
Two approaches can be followed for solving ab-initio crystal structures by powder diffraction data: the traditional approach and the direct space approach. Both ...
[59]
1FU2: FIRST PROTEIN STRUCTURE DETERMINED FROM X-RAY ...
Oct 16, 2000 · The first protein crystal structure determined from high-resolution X-ray powder diffraction data: a variant of T3R3 human insulin-zinc complex produced by ...
[60]
Learn: Guide to Understanding PDB Data: Crystallographic Data
In a typical crystallographic experiment, a crystal is subjected to a narrow beam of intense X-rays, and the diffraction pattern is observed with a detector or ...
[61]
12: Refining X-ray Crystal Structures - Books
Jul 24, 2019 · The symbol “wR2” is used to denote that the R-factor is weighted ... The values of R1 and wR2 decrease to 0.053 and 0.262, respectively ...
[62]
[PDF] The Resolution in X-ray Crystallography and Single-Particle ...
Jul 5, 2020 · There are numerous statistics for the quality of the data including, but not limited to, R-factors, signal-to-noise ratio (I/7) and completeness ...
[63]
The Powder Diffraction File: Past, Present, and Future - PMC
This paper reviews the development and growth of the PDF and discusses the role of the ICDD in the maintenance and dissemination of the file. Keywords: CD-ROM, ...
[64]
How Are Texture and Pole Figures Measured? - Rigaku
Traditional pole figure measurements are made by recording the intensity of a given Bragg reflection as a function of rotation and tilt of the sample.
[65]
Displaying texture - XRD - MyScope
The pole figure can be considered to be a map of crystal orientations with reference to the sample geometry. It shows how one crystal plane prefers to be ...
[66]
[PDF] Determination of Residual Stresses by X-ray Diffraction - Issue 2
There are two methods of rotating the sample when residual stress is measured by the sin2ψ technique: • The Omega Method. Here we rotate (tilt) the sample about ...Missing: sin²ψ | Show results with:sin²ψ
[67]
[PDF] X-Ray Diffraction Residual Stress Techniques - Lambda Technologies
Equation 7 and Fig. 3 show that if the lattice spacing, dθψ is a linear function of sin2ψ , the stress can be determined by measuring the lattice spacing.Missing: sin²ψ | Show results with:sin²ψ
[68]
[PDF] Back-to-Basics tutorial: X-ray diffraction of thin films
Oct 13, 2021 · X-ray diffraction (XRD) is an indispensable tool for characterising thin films of electroceramic materials. For the beginner, however, it can be ...
[69]
Grazing Incident X-ray Diffraction (GIXRD) and X-ray Reflectivity (XRR)
Apr 15, 2024 · An XRD instrument can be equipped with a Gobel (parabolic) mirror to produce parallel X-ray beams which results in less loss of X-ray ...
[70]
Polymorph screening - Rigaku
Polymorph screening uses X-ray diffraction (XRD) to identify different crystalline forms of a compound, which are distinct powder diffraction patterns.
[71]
A practical guide to pharmaceutical polymorph screening & selection
Powder X-ray diffraction (PXRD) is the front-line technology to analyze polymorphs. PXRD patterns between polymorphs are normally very distinct as compared ...
[72]
[PDF] Forensic Analysis of Geological Materials by Powder X-Ray ...
1.1 This guide covers techniques and procedures for the use of powder X-ray diffraction (XRD) in the forensic analysis of geological materials (to include soils ...
[73]
Identification of crystalline materials with X-Ray Diffraction (XRD)
XRD is a powerful tool for distinguishing between phases like hematite and magnetite based on the unique fingerprints from their crystal structures.
[74]
The time revolution in macromolecular crystallography - PMC
Apr 12, 2024 · Time-resolved crystallography is a new frontier, studying protein structure changes over time, using high-resolution to explore rapid dynamic ...
[75]
Time-resolved structural studies at synchrotrons and X-ray free ...
Aug 9, 2025 · We review recent time-resolved Laue diffraction and time-resolved wide angle X-ray scattering (WAXS) studies at synchrotron sources, and initial ...
[76]
Time-resolved structural studies with serial crystallography: A new ...
Jun 29, 2015 · Here, we describe the strategies towards structural dynamic studies of retinal proteins at room temperature, using injector or fixed-target ...
[77]
High-throughput and high-resolution powder X-ray diffractometer ...
The diffractometer is equipped with six sets of 2D CdTe detectors and an automation system including sample exchange and equipment switching.
[78]
Adaptively driven X-ray diffraction guided by machine learning for ...
Mar 2, 2023 · We validate the effectiveness of an adaptive approach by showing that ML-driven XRD can accurately detect trace amounts of materials in multi-phase mixtures ...
[79]
Autonomous robotic experimentation system for powder X-ray ...
Oct 14, 2024 · This system combines a robotic arm for precise sample preparation with machine learning-based techniques for automated data analysis. Our ...
[80]
The rise of the X-ray atomic pair distribution function method - NIH
Apr 29, 2019 · The atomic pair distribution function (PDF) technique is a powerful approach to gain quantitative insight into the structure of materials ...Missing: portable | Show results with:portable
[81]
Handheld X-ray Diffraction for Remote, Field-Based Applications
Jul 1, 2015 · This installment describes the development of two novel X-ray diffraction (XRD) techniques that enable the rapid analysis of samples using handheld ...
[82]
Review of Serial Femtosecond Crystallography including the COVID ...
Oct 27, 2023 · Serial femtosecond crystallography revolutionized macromolecular crystallography over the past decade by enabling the collection of X-ray ...
[83]
Advanced Mixed-Mode Pixel Array Detector for X-rays Above 20 keV ...
Jun 9, 2023 · This Final Technical Report summarizes progress made at Cornell University on novel integrating x-ray detectors that address these characteristics.
[84]
Radiation Damage in Macromolecular Crystallography—An ... - MDPI
Radiation damage still remains a major limitation and challenge in macromolecular X-ray crystallography. Some of the high-intensity radiation used for ...
[85]
Mechanisms and Mitigation of Radiation Damage in X-ray ...
Radiation damage by the illuminating X-rays limits the amount of structural information that can be obtained from protein and virus crystals, ...
[86]
X-Ray Crystallography - an overview | ScienceDirect Topics
However, X-ray crystallography does have limitations. It requires obtaining high-quality crystals, which can be challenging for some biomolecules, particularly ...Missing: diffractometers | Show results with:diffractometers
[87]
Solving Energy and Environmental Challenges with Synchrotron ...
Dec 14, 2020 · In addition to repairing a damaged environment, we have to characterize sources of damage such as CO2 and asbestos and develop catalysts and ...Missing: impact operations diffractometry
[88]
Structure of disordered materials under ambient to extreme ...
Structure of disordered materials under ambient to extreme conditions revealed by synchrotron x-ray diffraction techniques at SPring-8—recent ...<|separator|>
[89]
An overview of high‐throughput synthesis for advanced high ...
Feb 20, 2025 · By using machine learning, challenges such as data overload can be further alleviated, thereby significantly boosting experimental efficiency ...
[90]
Problems and Solutions in Quantitative Analysis of Complex ...
Mar 6, 2019 · The problems include particle statistics, primary extinction, microabsorption, preferred orientation, overlapping and broad reflections, ...Missing: challenges multiphase
[91]
Hybrid methods for macromolecular structure determination
This review describes recent approaches for building atomic models with a focus on X-ray diffraction and single-particle cryo-electron microscopy (cryo-EM) data ...Missing: diffractometry | Show results with:diffractometry
[92]
A tabletop neutron source | Nature
Feb 6, 2013 · The researchers' technique used less than one-quarter of the laser energy and generated an order of magnitude more neutrons in a forward ...
[93]
AI-enhanced X-ray diffraction analysis: towards real-time mineral ...
AI, using CNNs, can revolutionize XRD analysis by reducing processing times and enabling ultrafast interpretation, potentially enabling real-time analysis.Missing: diffractometry | Show results with:diffractometry
[94]
Synchrotron science for sustainability: life cycle of metals in the ...
Synchrotron-based imaging and spectroscopy have been essential in establishing current understanding of elemental speciation in complex environmental systems ...<|control11|><|separator|>